Intuitively, the weight correlation means that if a weight is large in magnitude at initialization, it is likely to be large after training. The reason for such correlation is that the learning rate is too low and weight updating is slow. Such weight correlation is not desirable for DNN training and typically results in lower accuracy, as weights in a well-trained DNN should depend more on the location of those weights instead of initialization [1]}. Thus when such weight correlation is strong, the DNN accuracy will be lower, i.e., not well-trained.
